"How can the show do something by itself? How can this be correct?"
I think you are confusing agency (or cause) with grammar.
When I observe something as if it's performing an action, I can describe it as performing an action:
The alarm sounded.
The ball rolled down the hill.
The car ran over my foot.
The knife cut my finger.
The movie started.
Grammar doesn't care how or why something happens (or who or what ultimately causes something to happen). It only cares about what is observed to occur—or what is being described.
Whether or not a statement makes sense depends on how it's commonly used—and how much thought we give to the meaning behind it.
For instance, the movie has started is a true statement. Yes, a person did something to cause it to start—or it was on some kind of a timer (either mechanical or controlled by software) that caused it to start. But why the movie started doesn't change the fact that it did start.
It's also true that the movie has been started (by someone or something). Both statements can be made, and they would both be equally valid.
But, idiomatically, we normally just say the former. And most of the time we don't care about the agent behind the action. (Unless there is some reason to think about it.)